EP0154577A1 - Prestressed tress beam with elements in buckling state - Google Patents

Prestressed tress beam with elements in buckling state Download PDF

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Publication number
EP0154577A1
EP0154577A1 EP85400231A EP85400231A EP0154577A1 EP 0154577 A1 EP0154577 A1 EP 0154577A1 EP 85400231 A EP85400231 A EP 85400231A EP 85400231 A EP85400231 A EP 85400231A EP 0154577 A1 EP0154577 A1 EP 0154577A1
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EP
European Patent Office
Prior art keywords
elementary
mesh
bars
elements
beam according
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Granted
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EP85400231A
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German (de)
French (fr)
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EP0154577B1 (en
Inventor
Michel Antoine Maistre
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Societe Europeenne de Propulsion SEP SA
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Europeenne De Propulsion SA Ste
Societe Europeenne de Propulsion SEP SA
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    • E—FIXED CONSTRUCTIONS
    • E04—BUILDING
    • E04H—BUILDINGS OR LIKE STRUCTURES FOR PARTICULAR PURPOSES; SWIMMING OR SPLASH BATHS OR POOLS; MASTS; FENCING; TENTS OR CANOPIES, IN GENERAL
    • E04H12/00—Towers; Masts or poles; Chimney stacks; Water-towers; Methods of erecting such structures
    • E04H12/16—Prestressed structures
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B64—AIRCRAFT; AVIATION; COSMONAUTICS
    • B64G—COSMONAUTICS; VEHICLES OR EQUIPMENT THEREFOR
    • B64G99/00—Subject matter not provided for in other groups of this subclass
    • E—FIXED CONSTRUCTIONS
    • E04—BUILDING
    • E04B—GENERAL BUILDING CONSTRUCTIONS; WALLS, e.g. PARTITIONS; ROOFS; FLOORS; CEILINGS; INSULATION OR OTHER PROTECTION OF BUILDINGS
    • E04B1/00—Constructions in general; Structures which are not restricted either to walls, e.g. partitions, or floors or ceilings or roofs
    • E04B1/18—Structures comprising elongated load-supporting parts, e.g. columns, girders, skeletons
    • E04B1/19—Three-dimensional framework structures
    • E—FIXED CONSTRUCTIONS
    • E04—BUILDING
    • E04B—GENERAL BUILDING CONSTRUCTIONS; WALLS, e.g. PARTITIONS; ROOFS; FLOORS; CEILINGS; INSULATION OR OTHER PROTECTION OF BUILDINGS
    • E04B1/00—Constructions in general; Structures which are not restricted either to walls, e.g. partitions, or floors or ceilings or roofs
    • E04B1/18—Structures comprising elongated load-supporting parts, e.g. columns, girders, skeletons
    • E04B1/19—Three-dimensional framework structures
    • E04B2001/1924—Struts specially adapted therefor
    • E04B2001/1927—Struts specially adapted therefor of essentially circular cross section
    • E—FIXED CONSTRUCTIONS
    • E04—BUILDING
    • E04B—GENERAL BUILDING CONSTRUCTIONS; WALLS, e.g. PARTITIONS; ROOFS; FLOORS; CEILINGS; INSULATION OR OTHER PROTECTION OF BUILDINGS
    • E04B1/00—Constructions in general; Structures which are not restricted either to walls, e.g. partitions, or floors or ceilings or roofs
    • E04B1/18—Structures comprising elongated load-supporting parts, e.g. columns, girders, skeletons
    • E04B1/19—Three-dimensional framework structures
    • E04B2001/1957—Details of connections between nodes and struts
    • E04B2001/1972—Welded or glued connection
    • E—FIXED CONSTRUCTIONS
    • E04—BUILDING
    • E04B—GENERAL BUILDING CONSTRUCTIONS; WALLS, e.g. PARTITIONS; ROOFS; FLOORS; CEILINGS; INSULATION OR OTHER PROTECTION OF BUILDINGS
    • E04B1/00—Constructions in general; Structures which are not restricted either to walls, e.g. partitions, or floors or ceilings or roofs
    • E04B1/18—Structures comprising elongated load-supporting parts, e.g. columns, girders, skeletons
    • E04B1/19—Three-dimensional framework structures
    • E04B2001/1981—Three-dimensional framework structures characterised by the grid type of the outer planes of the framework
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y10—TECHNICAL SUBJECTS COVERED BY FORMER USPC
    • Y10S—TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y10S52/00—Static structures, e.g. buildings
    • Y10S52/10—Polyhedron

Definitions

  • the present invention relates to a truss beam, and more precisely a beam of the type formed by regular repetition along the axis of the beam of polyhedral elementary meshes each having two identical parallel end faces in the form of regular polygons with n sides. which constitute the common faces with the neighboring meshes.
  • Lattice beams are commonly used as structural elements for the construction of buildings, structures and various materials such as cranes, pylons, antennas, etc.
  • They are elongated in shape and strongly perforated. They are generally formed by the assembly of rigid elements of elongated shape (bars) constituting a stable three-dimensional network (trellis).
  • the mesh sometimes includes, in addition to the rigid elements, flexible elements (cables) which, in general, brace the rigid elements and thus participate in the rigidity of the assembly.
  • the quality sought in the design and sizing of a truss beam is generally the best compromise between the three major properties: the tolerable load limits, acceptable deformations and mass. Other considerations frequently arise, particularly in terms of price, longevity, safety, etc.
  • the beam object of the invention is intended especially, but not exclusively, for the construction of very large arachnean structures which must constitute the framework of gigantic antennas, collectors of solar energy and other devices that we plan to erect in interplanetary space and especially in orbit around the earth.
  • the present invention aims to provide a truss beam particularly suitable for the realization of large spatial structures.
  • the elements which materialize the edges of the elementary mesh can be non-rigid since they are normally stressed only in traction. It is therefore possible to use flexible or articulated elements such as cables or chains.
  • the bars in buckling state are obtained from solid or hollow rectilinear elements with constant section.
  • the bars are tubular with a circular cross section.
  • connection of each bar with the elements stretched at the top of the mesh is comparable to a point support or an all-round articulation such as a ball joint, so that at this point the orientation of the bar is indifferent to the orientation of the stretched elements.
  • connection of each bar with the other bars of the mesh in the center of the latter is rigid so that the relative orientation of the bars with respect to each other in the vicinity of the competition point is frozen in a defined state by the theoretical geometry of the mesh.
  • the length of these bars is slightly greater than the distance between a vertex and the center of the polyhedron so that the assembly as described is only possible by bending the bars in an arc. Given the nature and orientation of the force supported by each bar (compression - following an axis passing through the two ends of the bar) this deformation corresponds to buckling. The rigid link in the center ensures the simultaneous buckling of all the bars.
  • the beam is designed so as to be normally stressed only in pure compression or in pure tension, which does not exclude that it can also withstand bending or torsional forces.
  • the application of compression or tension forces must be done as fairly as possible on the n vertices of the end faces of the beam and in a direction as parallel as possible to its axis.
  • the beam is terminated at each of its ends by a bundle of n bars starting from the n vertices of the last end face of elementary mesh and competing at a common point located on the axis of the beam.
  • the polyhedral elementary mesh with triangular lateral faces has its parallel and identical end faces, but offset with respect to each other by an angle 1T / n around the axis of the beam.
  • the elementary mesh is octahedral with triangular end faces.
  • the beam (10, Figure 1) is manufactured with "stretched elements" of circular section in a composite material based on carbon fibers and epoxy resin having a density of 1500kg per cubic meter and a modulus of elasticity in the longitudinal direction of 106GPa and with bars in the shape of tubes of circular section whose wall measures 0.71mm thick and made of the same material as the stretched elements.
  • This beam is formed by 31 identical meshes (11) in the shape of an octahedron 57.2cm high and by two end bundles (12) each constituted by three bars (13) of a section identical to those which it will be question and of a length such that each beam has a height of 28.4cm.
  • the octahedral meshes (11) are delimited by two triangular end faces formed by 3 stretched elements (14) 28.8cm long and 4.96mm in diameter, and by six lateral edges formed by stretched elements (15) 59.9mm long and 4.96mm in diameter.
  • the end faces of the same mesh are in the form of two equilateral triangles offset from each other by an angle of H / 3 around the axis of the beam (10).
  • All of these elements arranged along the edges of the octahedron are tensioned by a set of six bars (16) interposed between each of the vertices of the octahedron and its central point.
  • These hollow bars have an outside diameter of 9.36mm and an inner diameter of 7.94mm.
  • the rigid junction between the six bars (16) is ensured by a molded part (17, FIG. 2) made of aluminum alloy having the form of a bundle of six concurrent tubular ends with an internal diameter of 9 , 4mm in which the six bars are fitted.
  • the orientation of these six tips is defined by the orientation of the three diagonals of the octahedral mesh, that is to say that they make between them angles of 51 ° 19 'and, relative to the axis of symmetry mesh, angles of 30 0 .
  • Each vertex of the octahedron is common to two contiguous meshes. It is the meeting point of six stretched elements and two bars. The connection between these eight elements is ensured by a molded part (18, FIG. 3) made of aluminum alloy having the form of a bundle of six concurrent tubular ends with an internal diameter of 5.0 mm into which are fitted. with collage the six stretched elements.
  • the orientations of these six tips are defined by the orientations of the edges of two contiguous meshes, that is to say that they make angles of 60 ° between the two edges of the common face, of 27 0 48 'between two lateral edges of the same mesh and 76 ° 06 'between lateral edge and edge of the common face.
  • This part also has two convex spherical caps (18a) coated with a layer of rubber 1mm thick on which come to bear the ends of the two bars (16) which are provided at their end with a nozzle (16a) in the form of a concave spherical cap. These spherical caps have for common center the point of competition of the six ends which coincides with the top of the mesh.
  • the length of the bars (16) is such that it is 2% greater than the theoretical length available between this fulcrum and the bottom of the recess in the central connection piece (17), that is, in the present example 32.6cm against theoretical 32cm which has the effect that the bars (16) are all, and permanently, in the state of buckling and exert at the level vertices of the mesh of constant forces oriented so that they maintain all the elements (14,15) arranged along the edges in tension and this even when the beam is subjected to a compressive force between its extreme points up 'at the load limit of 4445N. Under this load, all of the side elements are completely relaxed and the beam fails without breaking or suffering irreversible damage.
  • This 18.3m long beam capable of withstanding a compressive force up to 4445N between its two extreme points weighs only 7.25kg which is broken down into 4.10kg of stretched elements, 1.85kg of bars and 1, 30kg of connection pieces. Under the limit load it shortens by 7.7mm or 0.042%.
  • This set of performances situates it favorably compared to a beam for large spatial structure produced with the same material according to conventional technology, that is to say in the form of a cylindrical tube of 17.2 cm in diameter and 0.71 mm. thick terminated by conical tips.
  • This reference beam equipped with tapered end pieces weighs 11.5 kg and is only shortened by 2mm or 0.011% under the limit load.
  • the beam of this example has the same characteristics as those of the first example except that the tensioned elements are made with a composite material made of carbon fibers and epoxy resin whose longitudinal modulus of elasticity is equal to 212GPa.
  • the diameter of these elements can be reduced to 3.5mm and the connecting pieces can also be reduced.
  • This beam capable of supporting the same limit load as the previous one weighs only 4.70 kg which is broken down into 2.05 kg of tensioned elements, 1.85 kg of bars and 0.80 kg of connecting pieces.
  • the beam of this example is manufactured with tensioned elements whose density and longitudinal elastic modulus are respectively 1500kg / m and 212GPa and with bars in the form of tubes whose wall measures 0.355mm thick and which are made with a material whose density and longitudinal elastic modulus are respectively 1500kg / m and 106GPa.
  • This beam is formed by 26 octahedral meshes 68.5 cm high and two end beams each consisting of three bars of a section identical to that which will be discussed and of a length such that each beam has a height 24.5cm.
  • the octahedral meshes are delimited by two triangular end faces formed by three stretched elements 34.3cm long and 2.95mm in diameter and by six lateral edges formed by stretched elements 71.3cm long and 2, 95mm in diameter.
  • the six bars have an outside diameter of 12.60mm and an inside diameter of 11.89mm. Their 38.8mm length is 2% greater than the theoretical length, so that they are in buckling state.
  • the connecting pieces are identical to those of the previous examples as regards the angles, but the diameters of the end pieces are adapted to the diameters of the tensioned elements and of the bars of the present example and they are made of magnesium alloy instead of aluminum.
  • This 18.3m long beam capable of withstanding a compression force up to 4445N between its two extreme points weighs only 3.35kg which is broken down into 1.45kg of stretched elements, 1.3kg of bars and 0, 6kg of connecting pieces.
  • the beam (20, Figure 4) of this example is formed of decahedral meshes (21).
  • the end faces are squares delimited by four elements stretched "crosswise” (24). These faces are connected by eight "lateral” stretched elements (25) which delimit eight triangular lateral faces.
  • the end faces of the same mesh being offset relative to each other by an angle of n / 4 around the axis of the beam (20).
  • the beam is formed of 18 identical meshes of 96cm in height and is terminated at each end by a bundle (22) of four concurrent bars (23) of a section identical to those which will be discussed and of a length such that each beam has a height of 51cm.
  • the tensioned elements (24.25) constituting the edges of the decahedral meshes have a diameter of 3.06 mm.
  • the "cross” elements (24) have a length of 35.3 cm while the “side” elements (25) have a length of 97.9 cm. All these tensioned elements are made of a composite material based on boron fibers and an epoxy resin whose density and elasticity modulus are respectively 1500kg / m 3 and 212GPa.
  • All of these elements arranged along the edges of the decahedron are tensioned by a set of eight bars (26) interposed between each of the vertices of the decahedron and its central point.
  • These tubular bars have an outside diameter. 13.56mm and an inner diameter of 12.85mm, they are made of a composite material based on boron fibers and an epoxy resin whose density and elastic modulus are respectively 1500kg / m 3 and 106GPa.
  • the length of these bars is equal to 53.0 cm, that is 1% more than the theoretical distance of 52.5 cm existing between the bottom of the recess in the central connecting piece and the fulcrum on the connecting piece of the elements stretched at the top of the decahedron.
  • the central connecting piece (27) is made of magnesium alloy and has eight concurrent tubular ends with an internal diameter of 13.6mm in which the eight bars are fitted.
  • the orientation of these eight tips is defined by the orientation of the eight straight lines connecting the central point of the decahedron to each of its vertices. Each thus makes an angle of 27 ° 31 ′ with respect to the axis of symmetry of the part and angles of 38 ° 08 ′ with respect to its two closest neighbors.
  • Each top of the decahedron is common to two contiguous meshes. It is the meeting point of six stretched elements and two bars.
  • the connection between these eight elements is ensured by a molded part (28) of magnesium alloy having the form of a bundle of six concurrent tubular ends with an internal diameter of 3.1 mm in which are fitted with bonding the six stretched elements.
  • the orientations of these six tips are defined by the orientations of the edges of the two contiguous meshes, that is to say that they make angles of 90 ° between the two edges of the common face, of 20 ° 48 'between two edges lateral of the same mesh and 79 ° 36 'between lateral edges and edges of the common face.
  • the two bars come to bear on this part on spherical caps as described in the first example.
  • This 18.3m long decahedral mesh beam capable of withstanding a compressive force up to 4445N between its two extreme points weighs only 4.38kg which is broken down into 1.95kg of tensioned elements, 1.83kg bars and 0.60 kg of connecting pieces. Under the limit load, it shortens by 6.8mm or 0.037%.
  • the prestressed beam object of the invention characterized by its structure made of the juxtaposition of identical polyhedral meshes delimited by elements tensioned by a set of bars competing at the central point of each mesh and by the fact that the The set of bars is in the buckling state can take other shapes and dimensions than those described here, be made of other materials and be used for other purposes.
  • the beam can thus be stressed in tension and it is able to withstand at the limit a tensile force much greater than the limit compressive force.
  • the octahedral mesh beams of examples 1, 2 and 3 are able to withstand a tensile force of 13335N at the limit while the decahedral mesh beam of example 4 is capable of withstanding the tensile force at the limit from 25900N.

Abstract

La poutre est formée par la répétition régulière le long de l'axe de la poutre de mailles élémentaires polyédriques (11) ayant chacune deux faces d'extrémité parallèles identiques en forme de polygones réguliers à n côtés qui constituent les faces communes avec les mailles voisines, et 2n faces latérales triangulaires formées en reliant chaque sommet d'une face d'extrémité aux deux plus proches sommets de la face d'extrémité opposée ; les arêtes de la maille élémentaire sont matérialisées par des éléments (14, 15) qui sont en permanence sollicités en traction, tandis que des barres rigides (16) en état de flambage relient chaque sommet de la maille élémentaire à son centre.The beam is formed by the regular repetition along the axis of the beam of polyhedral elementary meshes (11) each having two identical parallel end faces in the form of regular polygons with n sides which constitute the common faces with the neighboring meshes. , and 2n triangular lateral faces formed by connecting each vertex of an end face to the two closest vertices of the opposite end face; the edges of the elementary mesh are materialized by elements (14, 15) which are permanently stressed in tension, while rigid bars (16) in buckling state connect each top of the elementary mesh to its center.

Description

La présente invention concerne une poutre treillis, et plus précisément une poutre du type formé par la répétition régulière le long de l'axe de la poutre de mailles élémentaires polyèdriques ayant chacune deux faces d'extrémité parallèles identiques en forme de polygones réguliers à n côtés qui constituent les faces communes avec les mailles voisines.The present invention relates to a truss beam, and more precisely a beam of the type formed by regular repetition along the axis of the beam of polyhedral elementary meshes each having two identical parallel end faces in the form of regular polygons with n sides. which constitute the common faces with the neighboring meshes.

Les poutres treillis sont communément utilisées comme éléments de charpente pour la construction de bâtiments, d'ouvrages d'art et de matériels divers tels que grues, pylones, antennes, etc...Lattice beams are commonly used as structural elements for the construction of buildings, structures and various materials such as cranes, pylons, antennas, etc.

Elles sont de forme allongée et d'aspect fortement ajouré. Elles sont en général formées de l'assemblage d'éléments rigides de forme allongée (barres) constituant un réseau tridimensionnel stable (treillis).They are elongated in shape and strongly perforated. They are generally formed by the assembly of rigid elements of elongated shape (bars) constituting a stable three-dimensional network (trellis).

Le treillis comporte parfois, outre les éléments rigides, des éléments souples (câbles) qui, en général, entretoisent les éléments rigides et participent ainsi à la rigidité de l'ensemble.The mesh sometimes includes, in addition to the rigid elements, flexible elements (cables) which, in general, brace the rigid elements and thus participate in the rigidity of the assembly.

La qualité recherchée dans la conception et le dimensionnement d'une poutre treillis est en général le meilleur compromis entre les trois propriétés majeures : les charges limites supportables, les déformations acceptables et la masse. D'autres considérations interviennent fréquemment, notamment au niveau du prix, de la longévité, de la sécurité, etc...The quality sought in the design and sizing of a truss beam is generally the best compromise between the three major properties: the tolerable load limits, acceptable deformations and mass. Other considerations frequently arise, particularly in terms of price, longevity, safety, etc.

Le choix d'une structure de poutre treillis et de ses dimensions dépend aussi fortement du domaine dans lequel elle doit être utilisée et des sollicitations qu'elle doit supporter non seulement en service normal mais également dans des conditions de service accidentelles ou exceptionnelles.The choice of a truss structure and its dimensions also depends strongly on the field in which it must be used and the stresses which it must bear not only in normal service but also in accidental or exceptional service conditions.

La poutre objet de l'invention est destinée spécialement, mais non exclusivement, à la construction de très grandes structures arachnéennes qui doivent constituer la charpente de gigantesques antennes, de collecteurs d'énergie solaire et d'autres dispositifs qu'on envisage d'ériger dans l'espace interplanétaire et spécialement en orbite autour de la terre.The beam object of the invention is intended especially, but not exclusively, for the construction of very large arachnean structures which must constitute the framework of gigantic antennas, collectors of solar energy and other devices that we plan to erect in interplanetary space and especially in orbit around the earth.

Les dimensions de ces constructions, connues sous le vocable de "grandes structures spatiales" se chiffrent couramment, selon les projets étudiés, en centaines, voire même en milliers de mètres.The dimensions of these constructions, known by the term "large spatial structures" are commonly calculated, depending on the projects studied, in hundreds, even even thousands of meters.

La présente invention a pour but de fournir une poutre treillis convenant particulièrement à la réalisation de grandes structures spatiales.The present invention aims to provide a truss beam particularly suitable for the realization of large spatial structures.

Ce but est atteint au moyen d'une poutre treillis du type indiqué en tête de la description et dans laquelle, conformément à l'invention:

  • - chaque maille est délimitée latéralement par 2n faces triangulaires formées en reliant chaque sommet d'une face d'extrémité aux deux plus proches sommets de la face d'extrémité opposée,
  • - les arêtes de la maille élémentaires sont réalisées par des éléments qui sont en permanence sollicités en traction, et
  • - des barres rigides en état de flambage relient chaque sommet de la maille élémentaire à son centre.
This object is achieved by means of a lattice beam of the type indicated at the head of the description and in which, in accordance with the invention:
  • - each mesh is delimited laterally by 2n triangular faces formed by connecting each vertex of an end face to the two closest vertices of the opposite end face,
  • the elementary mesh edges are produced by elements which are permanently stressed in tension, and
  • - rigid bars in buckling state connect each vertex of the elementary mesh to its center.

On obtient de la sorte une poutre treillis précontrainte dans laquelle la géométrie de chaque maille élémentaire est définie par les éléments formant les arêtes, ces éléments étant maintenus en tension par les barres à l'état de flambage qui constituent en outre un dispositif fortement déformable servant à ajuster et à équilibrer les efforts sur les câbles.In this way, a prestressed truss beam is obtained in which the geometry of each elementary mesh is defined by the elements forming the edges, these elements being held in tension by the bars in the buckling state which also constitute a highly deformable device serving to adjust and balance the forces on the cables.

L'application de la précontrainte au moyen de barres à l'état de flambage plutôt qu'avec des barres non déformées présente des avantages importants.The application of prestressing by means of bars in the buckling state rather than with non-deformed bars has significant advantages.

En effet, la mise en précontrainte d'une maille élémentaire à niveau souhaité est délicate à réaliser au moyen de barres non déformées. Il est d'abord nécessaire de disposer des barres aux propriétés identiques, ce qui impose des tolérances de fabrication étroites qui grèvent lourdement le coût de la poutre. Il est ensuite nécessaire de régler précisément la précontrainte lors de l'assemblage des éléments constitutifs de la poutre, ce qui soulève des difficultés considérables dans le cadre de l'application aux grandes structures spatiales.Indeed, the prestressing of an elementary mesh at the desired level is difficult to achieve by means of non-deformed bars. It is first necessary to have bars with identical properties, which imposes narrow manufacturing tolerances which weigh heavily on the cost of the beam. It is then necessary to precisely adjust the prestress during the assembly of the constituent elements of the beam, which raises considerable difficulties in the context of application to large spatial structures.

Ces inconvénients sont évités et le réglage de la précontrainte grandement simplifié par l'utilisation de barres à l'état de flambage, puisqu'il est bien connu que l'effort supporté par une barre est alors pratiquement constant quel que soit le niveau de déformation. La fabrication des barres peut donc s'accomoder de tolérances beaucoup plus larges et le montage de la poutre en vue d'atteindre le niveau de précontrainte souhaité est bien moins délicat.These drawbacks are avoided and the setting of the prestressing greatly simplified by the use of bars in the buckling state, since it is well known that the force supported by a bar is then practically constant whatever the level of deformation . The manufacture of the bars can therefore accommodate much wider tolerances and the mounting of the beam in order to reach the desired prestressing level is much less delicate.

Les éléments qui matérialisent les arêtes de la maille élémentaire peuvent être non rigides puisqu'ils ne sont normalement sollicités qu'en traction. Il est donc possible d'utiliser des éléments souples ou articulés tels que des câbles ou des chaînes.The elements which materialize the edges of the elementary mesh can be non-rigid since they are normally stressed only in traction. It is therefore possible to use flexible or articulated elements such as cables or chains.

Les barres en état de flambage sont obtenues à partir d'éléments rectilignes pleins ou creux à section constante. De préférence, les barres sont tubulaires à section transversale circulaire.The bars in buckling state are obtained from solid or hollow rectilinear elements with constant section. Preferably, the bars are tubular with a circular cross section.

La liaison de chaque barre avec les éléments tendus à un sommet de la maille est assimilable à un appui ponctuel ou à une articulation tous azimuths telle qu'une rotule, en sorte qu'en ce point l'orientation de la barre est indifférente à l'orientation des éléments tendus.The connection of each bar with the elements stretched at the top of the mesh is comparable to a point support or an all-round articulation such as a ball joint, so that at this point the orientation of the bar is indifferent to the orientation of the stretched elements.

Par contre, la liaison de chaque barre avec les autres barres de la maille au centre de celle-ci est rigide en sorte que l'orientation relative des barres les unes par rapport aux autres au voisinage du point de concours est figée dans un état défini par la géométrie théorique de la maille.On the other hand, the connection of each bar with the other bars of the mesh in the center of the latter is rigid so that the relative orientation of the bars with respect to each other in the vicinity of the competition point is frozen in a defined state by the theoretical geometry of the mesh.

La longueur de ces barres est un peu supérieure à la distance entre un sommet et le centre du polyèdre en sorte que l'assemblage tel que décrit n'est possible que moyennant l'incurvation des barres suivant un arc. Etant donné la nature et l'orientation de l'effort supporté par chaque barre (compression --suivant un -axe passant par les deux extrémités de la barre) cette déformation correspond à un flambage. La liaison rigide au centre assure le flambage simultané de toutes les barres.The length of these bars is slightly greater than the distance between a vertex and the center of the polyhedron so that the assembly as described is only possible by bending the bars in an arc. Given the nature and orientation of the force supported by each bar (compression - following an axis passing through the two ends of the bar) this deformation corresponds to buckling. The rigid link in the center ensures the simultaneous buckling of all the bars.

La poutre est conçue pour n'être sollicitée normalement qu'en compression pure ou en traction pure, ce qui n'exclut pas qu'elle puisse supporter également des efforts de flexion ou de torsion. L'application des efforts de compression ou de tension doit se faire le plus équitablement possible sur les n sommets des faces d'extrémité de la poutre et suivant une direction le plus parallèle possible à son axe.The beam is designed so as to be normally stressed only in pure compression or in pure tension, which does not exclude that it can also withstand bending or torsional forces. The application of compression or tension forces must be done as fairly as possible on the n vertices of the end faces of the beam and in a direction as parallel as possible to its axis.

A cet effet, la poutre est terminée à chacune de ses extrémités par un faisceau de n barres partant des n sommets de la dernière face d'extrémité de maille élémentaire et concourant en un point commun situé sur l'axe de la poutre.To this end, the beam is terminated at each of its ends by a bundle of n bars starting from the n vertices of the last end face of elementary mesh and competing at a common point located on the axis of the beam.

La maille élémentaire polyèdrique à faces latérales triangulaire a ses faces d'extrémité parallèles et identiques, mais décalées l'une par rapport à l'autre d'un angle 1T/n autour de l'axe de la poutre.The polyhedral elementary mesh with triangular lateral faces has its parallel and identical end faces, but offset with respect to each other by an angle 1T / n around the axis of the beam.

Dans sa forme la plus simple, la maille élémentaire est octaèdrique avec des faces d'extrémité triangulaires.In its simplest form, the elementary mesh is octahedral with triangular end faces.

Le dimensionnement de la maille élémentaire et des éléments qui la constituent, "éléments tendus" et "barres", se fait en fonction des propriétés finales recherchées et compte tenu des propriétés des matériaux utilisés en suivant les lois de la résistance des matériaux et spécialement les règles régissant le flambage des poutres et des barres.The dimensioning of the elementary mesh and of the elements which constitute it, "stretched elements" and "bars", is done according to the desired final properties and taking into account the properties of the materials used by following the laws of the resistance of the materials and especially the rules governing the buckling of beams and bars.

D'autres particularités de la poutre treillis conforme à l'invention ressortiront à la lecture de la description d'exemples de réalisation, faite ci-après, à titre indicatif mais non limitatif. On se référera aux dessins annexés sur lesquels:

  • - la figure 1 est une vue schématique d'un tronçon d'une poutre treillis selon l'invention à maille élémentaire octaèdrique,
  • - la figure 2 est une vue schématique d'une pièce de raccordement au centre de la maille élémentaire de la poutre illustrée par la figure 1,
  • - la figure 3 est une vue schématique d'une pièce de raccordement à chaque sommet de la maille élémentaire de la poutre illustrée par la figure 1, et
  • - la figure 4 est une vue schématique d'un tronçon d'une poutre treillis selon l'invention à maille élémentaire décaèdrique.
Other features of the trellis beam according to the invention will emerge on reading the description of exemplary embodiments, given below, for information but not limitation. Reference is made to the appended drawings in which:
  • FIG. 1 is a schematic view of a section of a truss beam according to the invention with an octahedral elementary mesh,
  • FIG. 2 is a schematic view of a connecting piece at the center of the elementary mesh of the beam illustrated in FIG. 1,
  • - Figure 3 is a schematic view of a part of connection to each vertex of the elementary mesh of the beam illustrated in FIG. 1, and
  • - Figure 4 is a schematic view of a section of a truss beam according to the invention with decahedral elementary mesh.

Les exemples qui vont suivre correspondent à diverses variantes d'un même problème. Il s'agit de dimensionner au plus juste en ce qui concerne la masse une poutre de 18,3m de long devant pouvoir supporter au maximum une charge de compression axiale de 4445 N.The examples which follow correspond to various variants of the same problem. It is a question of dimensioning with the most just as regards the mass a beam of 18.3m long having to be able to support at most a load of axial compression of 4445 N.

1er exemple1st example

La poutre (10, figure 1) est fabriquée avec des "éléments tendus" de section circulaire en un matériau composite à base de fibres de carbone et de résine époxy ayant une masse volumétrique de 1500kg par mètre cube et un module d'élasticité dans le sens longitudinal de 106GPa et avec des barres en forme de tubes de section circulaire dont la paroi mesure 0,71mm d'épaisseur et réalisés dans le même matériau que les éléments tendus. Cette poutre est formée de 31 mailles identiques (11) en forme d'octaèdre de 57,2cm de haut et de deux faisceaux d'extrémités (12) constitués chacun par trois barres (13) d'une section identique à celles dont il va être question et d'une longueur telle que chaque faisceau a une hauteur de 28,4cm.The beam (10, Figure 1) is manufactured with "stretched elements" of circular section in a composite material based on carbon fibers and epoxy resin having a density of 1500kg per cubic meter and a modulus of elasticity in the longitudinal direction of 106GPa and with bars in the shape of tubes of circular section whose wall measures 0.71mm thick and made of the same material as the stretched elements. This beam is formed by 31 identical meshes (11) in the shape of an octahedron 57.2cm high and by two end bundles (12) each constituted by three bars (13) of a section identical to those which it will be question and of a length such that each beam has a height of 28.4cm.

Les mailles octaèdriques (11) sont délimitées par deux faces d'extrémité triangulaires formées par 3 éléments tendus (14) de 28,8cm de long et de 4,96mm de diamètre, et par six arêtes latérales formées par des éléments tendus (15) de 59,9mm de long et de 4,96mm de diamètre. Comme le montre la figure 1, les faces d'extrémité d'une même maille sont en forme de deux triangles équilatéraux décalés l'un par rapport à l'autre d'un angle de H/3 autour de l'axe de la poutre (10).The octahedral meshes (11) are delimited by two triangular end faces formed by 3 stretched elements (14) 28.8cm long and 4.96mm in diameter, and by six lateral edges formed by stretched elements (15) 59.9mm long and 4.96mm in diameter. As shown in Figure 1, the end faces of the same mesh are in the form of two equilateral triangles offset from each other by an angle of H / 3 around the axis of the beam (10).

L'ensemble de ces éléments disposés suivant les arêtes de l'octaèdre est mis en tension par un ensemble de six barres (16) interposées entre chacun des sommets de l'octaèdre et son point central. Ces barres creuses ont un diamètre extérieur de 9,36mm et un diamètre intérieur de 7,94mm.All of these elements arranged along the edges of the octahedron are tensioned by a set of six bars (16) interposed between each of the vertices of the octahedron and its central point. These hollow bars have an outside diameter of 9.36mm and an inner diameter of 7.94mm.

Au point central, la jonction rigide entre les six barres (16) est assurée par une pièce moulée (17, figure 2) en alliage d'aluminium ayant la forme d'un faisceau de six embouts tubulaires concourants d'un diamètre intérieur de 9,4mm dans lesquels viennent s'encastrer les six barres. L'orientation de ces six embouts est définie par l'orientation des trois diagonales de la maille octaèdrique c'est-à-dire qu'elles font entre elles des angles de 51°19' et, par rapport à l'axe de symétrie de la maille, des angles de 300.At the central point, the rigid junction between the six bars (16) is ensured by a molded part (17, FIG. 2) made of aluminum alloy having the form of a bundle of six concurrent tubular ends with an internal diameter of 9 , 4mm in which the six bars are fitted. The orientation of these six tips is defined by the orientation of the three diagonals of the octahedral mesh, that is to say that they make between them angles of 51 ° 19 'and, relative to the axis of symmetry mesh, angles of 30 0 .

Chaque sommet de l'octaèdre est commun à deux mailles contigues. C'est le point de rencontre de six éléments tendus et de deux barres. Le raccordement entre ces huit éléments est assuré par une pièce moulée (18, figure 3) en alliage d'aluminium ayant la forme d'un faisceau de six embouts tubulaires concourants d'un diamètre intérieur de 5,0mm dans lesquels viennent s'emmancher avec collage les six éléments tendus.Each vertex of the octahedron is common to two contiguous meshes. It is the meeting point of six stretched elements and two bars. The connection between these eight elements is ensured by a molded part (18, FIG. 3) made of aluminum alloy having the form of a bundle of six concurrent tubular ends with an internal diameter of 5.0 mm into which are fitted. with collage the six stretched elements.

Les orientations de ces six embouts sont définies par les orientations des arêtes de deux mailles contigues, c'est-à-dire qu'elles font des angles de 60° entre les deux arêtes de la face commune, de 27048' entre deux arêtes latérales de la même maille et 76°06' entre arête latérale et arête de la face commune. Cette pièce présente en outre deux calottes sphériques convexes (18a) revêtues d'une couche de caoutchouc de 1mm d'épaisseur sur lesquelles viennent prendre appui les extrémités des deux barres (16) qui sont munies à leur extrémité d'un embout (16a) en forme de calotte sphérique concave. Ces calottes sphériques ont pour centre commun le point de concours des six embouts qui coincide avec le sommet de la maille.The orientations of these six tips are defined by the orientations of the edges of two contiguous meshes, that is to say that they make angles of 60 ° between the two edges of the common face, of 27 0 48 'between two lateral edges of the same mesh and 76 ° 06 'between lateral edge and edge of the common face. This part also has two convex spherical caps (18a) coated with a layer of rubber 1mm thick on which come to bear the ends of the two bars (16) which are provided at their end with a nozzle (16a) in the form of a concave spherical cap. These spherical caps have for common center the point of competition of the six ends which coincides with the top of the mesh.

La longueur des barres (16) est telle qu'elle est de 2% supérieure à la longueur théorique disponible entre ce point d'appui et le fond de l'encastrement dans la pièce de raccordement centrale (17), soit, dans l'exemple présent 32,6cm contre 32cm théorique ce qui a pour effet que les barres (16) sont toutes, et de façon permanente, à l'état de flambage et exercent au niveau des sommets de la maille des efforts constants orientés de telle sorte qu'ils maintiennent l'ensemble des éléments (14,15) disposés suivant les arêtes en tension et ceci même lorsque la poutre est soumise à un effort de compression entre ses pointes extrêmes jusqu'à la charge limite de 4445N. Sous cette charge, l'ensemble des éléments latéraux se trouvent complètement détendus et la poutre cède sans, pour autant, se rompre ou subir des dégâts irréversibles.The length of the bars (16) is such that it is 2% greater than the theoretical length available between this fulcrum and the bottom of the recess in the central connection piece (17), that is, in the present example 32.6cm against theoretical 32cm which has the effect that the bars (16) are all, and permanently, in the state of buckling and exert at the level vertices of the mesh of constant forces oriented so that they maintain all the elements (14,15) arranged along the edges in tension and this even when the beam is subjected to a compressive force between its extreme points up 'at the load limit of 4445N. Under this load, all of the side elements are completely relaxed and the beam fails without breaking or suffering irreversible damage.

Cette poutre de 18,3m de long capable de supporter un effort de compression jusqu'à 4445N entre ses deux points extrêmes ne pèse que 7,25kg qui se décomposent en 4,10kg d'éléments tendus, 1,85kg de barres et 1,30kg de pièces de raccordement. Sous la charge limite elle se raccourcit de 7,7mm soit 0,042%.This 18.3m long beam capable of withstanding a compressive force up to 4445N between its two extreme points weighs only 7.25kg which is broken down into 4.10kg of stretched elements, 1.85kg of bars and 1, 30kg of connection pieces. Under the limit load it shortens by 7.7mm or 0.042%.

Cet ensemble de performances la situe favorablement par rapport à une poutre pour grande structure spatiale réalisée avec le même matériau suivant la technologie classique c'est-à-dire sous forme d'un tube cylindrique de 17,2cm de diamètre et de 0,71mm d'épaisseur terminé par des embouts coniques. Cette poutre de référence équipée de pièces d'extrémités coniques pèse 11,5kg et ne se raccourcit que de 2mm soit 0,011% sous la charge limite.This set of performances situates it favorably compared to a beam for large spatial structure produced with the same material according to conventional technology, that is to say in the form of a cylindrical tube of 17.2 cm in diameter and 0.71 mm. thick terminated by conical tips. This reference beam equipped with tapered end pieces weighs 11.5 kg and is only shortened by 2mm or 0.011% under the limit load.

2ème exemple2nd example

La poutre de cet exemple a les mêmes caractéristiques que celles du premier exemple à part le fait que les éléments tendus sont réalisés avec un matériau composite fait de fibres de carbone et de résine époxy dont le module d'élasticité longitudinal est égal à 212GPa.The beam of this example has the same characteristics as those of the first example except that the tensioned elements are made with a composite material made of carbon fibers and epoxy resin whose longitudinal modulus of elasticity is equal to 212GPa.

De ce fait, le diamètre de ces éléments peut être réduit à 3,5mm et les pièces de raccordement peuvent être également allégées.Therefore, the diameter of these elements can be reduced to 3.5mm and the connecting pieces can also be reduced.

Cette poutre capable de supporter la même charge limite que la précédente ne pèse que 4,70kg qui se décomposent en 2,05kg d'éléments tendus, 1,85kg de barres et 0,80kg de pièces de raccordement.This beam capable of supporting the same limit load as the previous one weighs only 4.70 kg which is broken down into 2.05 kg of tensioned elements, 1.85 kg of bars and 0.80 kg of connecting pieces.

Elle se raccourcit sous la charge limite de la même valeur que la précédente.It is shortened under the limit load by the same value as the previous one.

3ème exemple3rd example

La poutre de cet exemple est fabriquée avec des éléments tendus dont la masse volumique et le module d'élasticité longitudinal valent respectivement 1500kg/m et 212GPa et avec des barres en forme de tubes dont la paroi mesure 0,355mm d'épaisseur et qui sont réalisés avec un matériau dont la masse volumique et le module d'élasticité longitudinal valent respectivement 1500kg/m et 106GPa.The beam of this example is manufactured with tensioned elements whose density and longitudinal elastic modulus are respectively 1500kg / m and 212GPa and with bars in the form of tubes whose wall measures 0.355mm thick and which are made with a material whose density and longitudinal elastic modulus are respectively 1500kg / m and 106GPa.

Cette poutre est formée de 26 mailles octaèdriques de 68,5cm de haut et de deux faisceaux d'extrémités constitués chacun par trois barres d'une section identique à celle dont il va être question et d'une longueur telle que chaque faisceau a une hauteur de 24,5cm.This beam is formed by 26 octahedral meshes 68.5 cm high and two end beams each consisting of three bars of a section identical to that which will be discussed and of a length such that each beam has a height 24.5cm.

Les mailles octaèdriques sont délimitées par deux faces d'extrémités triangulaires formées par trois éléments tendus de 34,3cm de long et de 2,95mm de diamètre et par six arêtes latérales formées par des éléments tendus de 71,3cm de long et de 2,95mm de diamètre.The octahedral meshes are delimited by two triangular end faces formed by three stretched elements 34.3cm long and 2.95mm in diameter and by six lateral edges formed by stretched elements 71.3cm long and 2, 95mm in diameter.

Les six barres ont un diamètre extérieur de 12,60mm et un diamètre intérieur de 11,89mm. Leur longueur de 38,8mm est supérieure de 2% à la longueur théorique, en sorte qu'elles sont en état de flambage.The six bars have an outside diameter of 12.60mm and an inside diameter of 11.89mm. Their 38.8mm length is 2% greater than the theoretical length, so that they are in buckling state.

Les pièces de raccordement sont identiques à celles des exemples précédents en ce qui concerne les angles mais les diamètres des embouts sont adaptés aux diamètres des éléments tendus et des barres du présent exemple et elles sont réalisées en alliage de magnésium au lieu d'aluminium.The connecting pieces are identical to those of the previous examples as regards the angles, but the diameters of the end pieces are adapted to the diameters of the tensioned elements and of the bars of the present example and they are made of magnesium alloy instead of aluminum.

Cette poutre de 18,3m de long capable de supporter un effort de compression jusqu'à 4445N entre ses deux points extrêmes ne pèse que 3,35kg qui se décomposent en 1,45kg d'éléments tendus, 1,3kg de barres et 0,6kg de pièces de raccordement.This 18.3m long beam capable of withstanding a compression force up to 4445N between its two extreme points weighs only 3.35kg which is broken down into 1.45kg of stretched elements, 1.3kg of bars and 0, 6kg of connecting pieces.

Elle se raccourcit de 10,8mm sous la charge limite soit 0,059%.It shortens by 10.8mm under the limit load, i.e. 0.059%.

4ème exemple4th example

La poutre (20, figure 4) de cet exemple est formée de mailles décaèdriques (21). Les faces d'extrémités sont des carrés délimités par quatre éléments tendus "travers" (24). Ces faces sont reliées par huit éléments tendus "latéraux" (25) qui délimitent huit faces latérales triangulaires. Les faces d'extrémités d'une même maille étant décalées l'une par rapport à l'autre d'un angle de n/4 autour de l'axe de la poutre (20).The beam (20, Figure 4) of this example is formed of decahedral meshes (21). The end faces are squares delimited by four elements stretched "crosswise" (24). These faces are connected by eight "lateral" stretched elements (25) which delimit eight triangular lateral faces. The end faces of the same mesh being offset relative to each other by an angle of n / 4 around the axis of the beam (20).

La poutre est formée de 18 mailles identiques de 96cm de hauteur et est terminée à chaque extrémité par un faisceau (22) de quatre barres concourantes (23) d'une section identique à celles dont il va être question et d'une longueur telle que chaque faisceau a une hauteur de 51cm.The beam is formed of 18 identical meshes of 96cm in height and is terminated at each end by a bundle (22) of four concurrent bars (23) of a section identical to those which will be discussed and of a length such that each beam has a height of 51cm.

Les éléments tendus (24,25) constituant les arêtes des mailles décaèdriques ont un diamètre de 3,06mm. Les éléments "travers" (24) ont une longueur de 35,3cm alors que les éléments "latéraux" (25) ont une longueur de 97,9cm. Tous ces éléments tendus sont constitués d'un matériau composite à base de fibres de bore et d'une résine époxy dont la masse volumique et le module d'élasticité valent respectivement 1500kg/m3 et 212GPa.The tensioned elements (24.25) constituting the edges of the decahedral meshes have a diameter of 3.06 mm. The "cross" elements (24) have a length of 35.3 cm while the "side" elements (25) have a length of 97.9 cm. All these tensioned elements are made of a composite material based on boron fibers and an epoxy resin whose density and elasticity modulus are respectively 1500kg / m 3 and 212GPa.

L'ensemble de ces éléments disposés suivant les arêtes du décaèdre est mis en tension par un ensemble de huit barres (26) interposées entre chacun des sommets du décaèdre et son point central. Ces barres tubulaires ont un diamètre extérieur. de 13,56mm et un diamètre intérieur de 12,85mm, elles sont constituées d'un matériau composite à base de fibres de bore et d'une résine époxy dont la masse volumique et le module d'élasticité valent respectivement 1500kg/m3 et 106GPa. La longueur de ces barres est égale à 53,0cm soit 1% de plus que la distance théorique de 52,5cm existant entre le fond de l'encastrement dans la pièce de liaison centrale et le point d'appui sur la pièce de raccordement des éléments tendus au sommet du décaèdre.All of these elements arranged along the edges of the decahedron are tensioned by a set of eight bars (26) interposed between each of the vertices of the decahedron and its central point. These tubular bars have an outside diameter. 13.56mm and an inner diameter of 12.85mm, they are made of a composite material based on boron fibers and an epoxy resin whose density and elastic modulus are respectively 1500kg / m 3 and 106GPa. The length of these bars is equal to 53.0 cm, that is 1% more than the theoretical distance of 52.5 cm existing between the bottom of the recess in the central connecting piece and the fulcrum on the connecting piece of the elements stretched at the top of the decahedron.

Cette surlongueur est suffisante pour assurer le flambage des barres. De plus, la liaison rigide des huit barres au point central impose que ce flambage se produise simultanément sur les huit barres.This extra length is sufficient to ensure the buckling of the bars. In addition, the rigid connection of the eight bars to the central point requires that this buckling occurs simultaneously on the eight bars.

La pièce de raccordement centrale (27) est réalisée en alliage de magnésium et présente huit embouts tubulaires concourants d'un diamètre intérieur de 13,6mm dans lesquels viennent s'encastrer les huit barres. L'orientation de ces huit embouts est définie par l'orientation des huit droites liant le point central du décaèdre à chacun de ses sommets. Chacun fait ainsi un angle de 27°31' par rapport à l'axe de symétrie de la pièce et des angles de 38°08' par rapport à ses deux plus proches voisins.The central connecting piece (27) is made of magnesium alloy and has eight concurrent tubular ends with an internal diameter of 13.6mm in which the eight bars are fitted. The orientation of these eight tips is defined by the orientation of the eight straight lines connecting the central point of the decahedron to each of its vertices. Each thus makes an angle of 27 ° 31 ′ with respect to the axis of symmetry of the part and angles of 38 ° 08 ′ with respect to its two closest neighbors.

Chaque sommet du décaèdre est commun à deux mailles contigues. C'est le point de rencontre de six éléments tendus et de deux barres. Le raccordement entre ces huit éléments est assuré par une pièce moulée (28) en alliage de magnésium ayant la forme d'un-faisceau de six embouts tubulaires concourants d'un diamètre intérieur de 3,1mm dans lesquels viennent s'emmancher avec collage les six éléments tendus. Les orientations de ces six embouts sont définies par les orientations des arêtes des deux mailles contigues c'est-à-dire qu'elles font des angles de 90° entre les deux arêtes de la face commune, de 20°48' entre deux arêtes latérales de la même maille et 79°36' entre arêtes latérales et arêtes de la face commune. Les deux barres viennent prendre appui sur cette pièce sur des calottes sphériques comme décrit dans le premier exemple.Each top of the decahedron is common to two contiguous meshes. It is the meeting point of six stretched elements and two bars. The connection between these eight elements is ensured by a molded part (28) of magnesium alloy having the form of a bundle of six concurrent tubular ends with an internal diameter of 3.1 mm in which are fitted with bonding the six stretched elements. The orientations of these six tips are defined by the orientations of the edges of the two contiguous meshes, that is to say that they make angles of 90 ° between the two edges of the common face, of 20 ° 48 'between two edges lateral of the same mesh and 79 ° 36 'between lateral edges and edges of the common face. The two bars come to bear on this part on spherical caps as described in the first example.

Cette poutre à mailles décaèdriques de 18,3m de long, capable de supporter un effort de compression jusqu'à 4445N entre ses-deux points extrêmes ne pèse que 4,38kg qui se décomposent en 1,95kg d'éléments tendus, 1,83kg de barres et 0,60kg de pièces de raccordement. Sous la charge limite, elle se raccourcit de 6,8mm soit 0,037%.This 18.3m long decahedral mesh beam, capable of withstanding a compressive force up to 4445N between its two extreme points weighs only 4.38kg which is broken down into 1.95kg of tensioned elements, 1.83kg bars and 0.60 kg of connecting pieces. Under the limit load, it shortens by 6.8mm or 0.037%.

Ces diverses versions d'une poutre de longueur donnée devant supporter à la limite une charge de compression donnée n'ont été présentées, à titre d'exemples, que pour illustrer la diversité des formes et des dimensions que peut prendre la poutre conforme à l'invention et dans quelle mesure cette poutre peut être plus légère qu'une poutre tubulaire classique ce qui est un avantage très précieux pour l'utilisation privilégiée envisagée en raison du coût du transport dans l'espace à partir de la terre.These various versions of a beam of given length having to bear at the limit a given compression load have been presented, by way of examples, only to illustrate the diversity of shapes and dimensions that the beam conforming to l can take. invention and to what extent this beam can be lighter than a conventional tubular beam which is a very valuable advantage for the preferred use envisaged because of the cost of transport in space from the ground.

Il va de soi que la poutre précontrainte objet de l'invention caractérisée par sa structure faite de la juxtaposition de mailles polyèdriques identiques délimitées par des éléments mis en tension par un ensemble de barres concourant au point central de chaque maille et par le fait que l'ensemble des barres est à l'état de flambage peut prendre d'autres formes et dimensions que celles décrites ici, être réalisées en d'autres matériaux et être affectée à d'autres usages.It goes without saying that the prestressed beam object of the invention characterized by its structure made of the juxtaposition of identical polyhedral meshes delimited by elements tensioned by a set of bars competing at the central point of each mesh and by the fact that the The set of bars is in the buckling state can take other shapes and dimensions than those described here, be made of other materials and be used for other purposes.

On s'est attaché, dans les exemples traités à satisfaire essentiellement une exigence de tenue en compression car c'est en général la caractéristique la plus critique pour ce genre de poutre mais ceci n'exclut pas pour une telle poutre la possibilité de supporter des efforts d'autre nature tels que traction, torsion ou flexion.In the examples treated, we have endeavored to essentially satisfy a requirement of compressive strength because it is generally the most critical characteristic for this type of beam, but this does not exclude for such a beam the possibility of supporting other efforts such as traction, torsion or bending.

L'application d'un effort de traction sur toute la longueur de la poutre suppose que les faisceaux d'extrémité soient eux mêmes capables de transmettre ces efforts au treillis formé par les éléments tendus. Il faut pour cela que les barres constituant ces faisceaux d'extrémités soient convenablement verrouillées sur les pièces de raccordement des éléments tendus où ils aboutissent, ce qui ne pose aucun problème.The application of a tensile force over the entire length of the beam assumes that the end beams are themselves capable of transmitting these forces to the trellis formed by the tensioned elements. This requires that the bars constituting these end bundles are properly locked on the connecting pieces of the tensioned elements where they end, which poses no problem.

La poutre peut ainsi être sollicitée en traction et elle est capable de supporter à la limite un effort de traction très supérieur à l'effort de compression limite. Ainsi, les poutres à mailles octaédriques des exemples 1, 2 et 3 sont capables de supporter à la limite un effort de traction de 13335N tandis que la poutre à mailles décaédriques de l'exemple 4 est capable de supporter à la limite un effort de traction de 25900N.The beam can thus be stressed in tension and it is able to withstand at the limit a tensile force much greater than the limit compressive force. Thus, the octahedral mesh beams of examples 1, 2 and 3 are able to withstand a tensile force of 13335N at the limit while the decahedral mesh beam of example 4 is capable of withstanding the tensile force at the limit from 25900N.

Claims (10)

1. Poutre treillis formée par la répétition régulière le long de l'axe de la poutre de mailles élémentaires polyédriques ayant chacune deux faces d'extrémité parallèles identiques en forme de polygones réguliers à n côtés qui constituent les faces communes avec les mailles voisines, caractérisée en ce que : - chaque maille (11, 21) est délimitée latéralement par 2n faces triangulaires formées en reliant chaque sommet d'une face d'extrémité aux deux plus proches sommets de la face d'extrémité opposée, - les arêtes de la maille élémentaire sont matérialisées par des éléments (14, 15 ; 24, 25) qui sont en permanence sollicités en traction, et - des barres rigides (16, 26) en état de flambage relient chaque sommet de la maille élémentaire à son centre. 1. Lattice beam formed by regular repetition along the axis of the beam of polyhedral elementary meshes each having two identical parallel end faces in the form of regular polygons with n sides which constitute the common faces with the neighboring meshes, characterized in that : each mesh (11, 21) is delimited laterally by 2n triangular faces formed by connecting each vertex of an end face to the two closest vertices of the opposite end face, the edges of the elementary mesh are materialized by elements (14, 15; 24, 25) which are permanently stressed in traction, and - Rigid bars (16, 26) in buckling state connect each top of the elementary mesh to its center. 2. Poutre selon la revendication 1, caractérisée en ce que chaque barre à l'état de flambage a une extrémité reliée rigidement aux autres barres de la même maille élémentaire au centre de celle-ci et l'autre extrémité articulée à un sommet de la maille.2. Beam according to claim 1, characterized in that each bar in the buckling state has one end rigidly connected to the other bars of the same elementary mesh in the center thereof and the other end hinged to a top of the mesh. 3. Poutre selon la revendication 2, caractérisée en ce que chaque sommet de maille élémentaire est matérialisé par une pièce de raccordement (18, 28) comprenant six logements pour les extrémités des éléments tendus (14, 15 ; 24, 25) concourant à ce sommet, et deux surfaces d'appui pour des surfaces d'extrémité des barres (16, 26) reliant le sommet aux centres des deux mailles élémentaires auxquelles ce sommet est commun.3. Beam according to claim 2, characterized in that each elementary mesh top is materialized by a connecting piece (18, 28) comprising six housings for the ends of the tensioned elements (14, 15; 24, 25) contributing to this apex, and two bearing surfaces for end surfaces of the bars (16, 26) connecting the apex to the centers of the two elementary meshes to which this apex is common. 4. Poutre selon la revendication 3, caractérisée en ce que lesdites surfaces d'appui (18a) et surfaces d'extrémité (16a) ont la forme de calottes sphériques.4. Beam according to claim 3, characterized in that said bearing surfaces (18a) and end surfaces (16a) have the shape of spherical caps. 5. Poutre selon l'une quelconque des revendications 1 à 4, caractérisée en ce qu'elle est terminée à chacune de ses extrémités par un_ faisceau (12, 22) de n barres (13, 23) partant des n sommets de la dernière face d'extrémité de maille élémentaire et concourant en un point situé sur l'axe de la poutre.5. Beam according to any one of claims 1 to 4, characterized in that it is terminated at each of its ends by a beam (12, 22) of n bars (13, 23) starting from the n vertices of the last mesh end face elementary and concurrent at a point located on the axis of the beam. 6. Poutre selon l'une quelconque des revendications 1 à 5, caractérisée en ce que les éléments qui matérialisent les arêtes de la maille élémentaire sont non rigides.6. Beam according to any one of claims 1 to 5, characterized in that the elements which materialize the edges of the elementary mesh are non-rigid. 7. Poutre selon l'une quelconque des revendications 1 à 6, caractérisée en ce que les barres (16, 26) qui relient chaque sommet d'une maille élémentaire au centre de celle-ci sont des éléments tubulaires à section circulaire.7. Beam according to any one of claims 1 to 6, characterized in that the bars (16, 26) which connect each vertex of an elementary mesh in the center thereof are tubular elements with circular section. 8. Poutre selon l'une quelconque des revendications 1 à 7, caractérisée en ce que les mailles élémentaires (11) sont octaédriques avec deux faces d'extrémité triangulaires décalées l'une par rapport à l'autre d'un angle de n/3 autour de l'axe de la poutre (10).8. Beam according to any one of claims 1 to 7, characterized in that the elementary meshes (11) are octahedral with two triangular end faces offset relative to each other by an angle of n / 3 around the axis of the beam (10). 9. Poutre selon l'une quelconque des revendications 1 à 8, caractérisée en ce que les mailles élémentaires (21) sont décaédriques avec deux faces d'extrémité carrées décalées l'une par rapport à l'autre d'un angle de
Figure imgb0001
/4 autour de l'axe de la poutre (20).9. Beam according to any one of claims 1 to 8, characterized in that the elementary meshes (21) are decahedral with two square end faces offset from one another by an angle of
Figure imgb0001
/ 4 around the axis of the beam (20). 10. Utilisation d'une poutre selon l'une quelconque des revendications 1 à 9, pour la construction de grandes structures spatiales.10. Use of a beam according to any one of claims 1 to 9, for the construction of large spatial structures.
EP85400231A 1984-02-20 1985-02-13 Prestressed tress beam with elements in buckling state Expired EP0154577B1 (en)

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FR8402525A FR2559813B1 (en) 1984-02-20 1984-02-20 PRESTRESSED MESH BEAM WITH ELEMENTS IN FLAMMING CONDITION
FR8402525 1984-02-20

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US4612750A (en) 1986-09-23
CA1249411A (en) 1989-01-31
EP0154577B1 (en) 1988-09-21
FR2559813B1 (en) 1987-08-07
JPS60195250A (en) 1985-10-03
DE3565141D1 (en) 1988-10-27

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